486

Part of 1988 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 486 All Soviet Union MO 1988 r < ab/( 2(a + b) ) inradius of tetrahedron

Source:

Prove that for any tetrahedron the radius of the inscribed sphere

r <\frac{ ab}{ 2(a + b)}

a

b

are the lengths of any pair of opposite edges.

spheretetrahedronradicalgeometric inequality3D geometrygeometry